The conventional steady state RTE governs light propagation in the diffuse
medium, such as, e.g. turbulent atmosphere and biological media [1]}. Inverse problems for RTE have applications in, e.g. problems of seeing
through a turbulent atmosphere and in an early medical diagnostics. In the
latter case the near infrared light with a relatively small energy of
photons is used, see, e.g. [2]}, [3]}. However, it is assumed in RTE that
photons propagate along straight lines between their collisions. On the
other hand, since the dielectric constants in heterogeneous media, such as,
e.g. ones mentioned above, vary in space, then photons actually propagate
along geodesic lines between their collisions. These lines are generated by
the Riemannian metric \(\sqrt{\varepsilon _{r}\left( \mathbf {x}\right) }\left|d\mathbf {x}\right|.\)  Here and below \(\mathbf {x}=\left(x,y,z\right) \in \mathbb {R}^{3}\)  and \(\varepsilon _{r}\left( \mathbf {x}\right) \)  is the spatially distributed dielectric constant, so  that \(n\left( \mathbf {x}\right) =\sqrt{\varepsilon _{r}\left( \mathbf {x}\right) }\) 
is the refractive index. To take this into account, the so-called Riemannian
Radiative Transport Equation (RRTE) should be used.
